Question

Wine-pouring vending machines, previously available in Europe and international airports, have become popular in the last few years in the United States. They are even approved to dispense wine in some Wal-Mart stores. The available pouring options are a 5-ounce glass, a 2.5-ounce half-glass, and a 1-ounce taste. When the machine is in statistical control (see Exercise 7.42), the amount dispensed for a full glass is 5.1 ounces. Four observations are taken each day, to plot a daily mean over time on a control chart to check for irregularities. The most recent day’s observations were 5.05, 5.15, 4.95, and 5.11. Could the difference between the sample mean and the target value be due to random variation, or can you conclude that the true mean is now different from 5.1? Answer by showing the five steps of a significance test, making a decision using a 0.05 significance level.